"When I had satisfied myself that no star of that kind had ever shone before, I was led into such perplexity by the unbelievability of the thing that I began to doubt the faith of my own eyes." -Tycho Brahe When stars reach the end of their lives, there are many possible fates that they can have. Among the most spectacular, however, are stars that end their lives by going supernova, where a single star can outshine even an entire galaxy for a brief moment in time.
(Image credit: SN 2006gy, X-ray by NASA / CXC, Nathan Smith, Weidong Li et al., IR by PAIRITEL / Lick / U.C. Berkeley / J.Bloom, and C.Hansen.)
Although it isn't nearly as spectacular as what we'd get to see if we experienced another supernova within our own galaxy, a phenomenon not experienced on Earth since 1604!
(Image credit: Stellarium.)
When they occur within our own galaxy, supernovae are so bright that they outshine all the other stars, all the planets, and can often even be seen during the day. They're very rare, though, occurring less than once per century, on average, in our own galaxy.
But there are other galaxies that have better luck than we do.
(Image credit: NASA, ESA, and The Hubble Heritage Team (STScI/AURA).)
Many galaxies, unlike our own, are actively forming large quantities of stars! In many spiral galaxies, like NGC 1672, above, pink regions can line the arms of galaxies, surefire evidence of recent, intense star formation. Recent mergers, including the gobbling up of small, satellite galaxies, as well as simply the density waves of spiral arms can often trigger this type of star formation all on their own.
But when galaxies gravitationally interact with one another -- even when separated by millions of light years -- they can intensify this ongoing star formation.
With this in mind, let me introduce you to one of the nearer galaxies in our night sky: Messier 95 (M95).
(Image credit: Paul and Liz Downing.)
Messier 95 is a spiral galaxy, with strong inner arms and faint outer arms, located 38 million light years away. It's also very close to Messier 96, and Messier 105; together, with a few other galaxies, they form a group! The image below, created by me with Stellarium, shows the entire group, all contained within just a single degree in the night sky.
You'll also notice, in the upper right of the image, lies the planet Mars.
Shining brightly in the night sky, Mars, in many locations, is the brightest object visible in the sky during much of the night. It doesn't look like it, in the image above, because I've artificially reduced its brightness by a factor of many thousands. Normally, astronomical observers look for the following traits when they go to take their observations:
- clear, dark skies,
- far away from any sources of light pollution,
- a moonless night, and for the most hardcore,
- high altitudes (to limit atmospheric interference).
(Image credit: Jim Misti / Map created with Stellarium, retrieved from Astro Bob.)
Messier 95 is located less than half-a-degree away from Mars in the night sky, but appears to be about 100,000 times less bright than the red planet right now. On the magnitude scale (smaller is brighter), M95 is magnitude 9.7, while Mars is of magnitude negative one.
But you'll want to see Messier 95 now, because in a region of that galaxy that contained absolutely nothing, a very bright object suddenly appeared just four days ago, and is increasing in brightness; it's got to be a supernova! Zooming in on the earlier image of M95, I want to show you exactly where you should look if you want to see it; anyone with an 8" telescope or bigger (and the proper magnification -- 100x for an 8") should be able to find it! (But no smaller than a 6" under the best of circumstances for now; you'll waste your time looking for it.)
(Image credit: Paul and Liz Downing, marked by me.)
At this point, we haven't officially determined whether it's a type Ia supernova (formed by an exploding ancient white dwarf) or a type II supernova (formed from a very massive, young star that's finished burning its nuclear fuel), but look at the location: it's right on one of the outer spiral arms! That's one of the key places where young, massive stars form, and so just by looking at that, I can tell you that it's almost definitely a type II supernova.
Want to know what it looks like through a telescope? Take a look, below.
(Image credit: Nik Szymanek.)
As you can see, marked by the lines, there's a fairly distinct object that looks like a star within our own galaxy. But that's not a Milky Way star, a few hundred or a few thousand light years away, but a supernova in Messier 95, located 38 million light years distant! Over the coming weeks, the supernova will continue to brighten, and will be more clearly visible and more easily seen. But one thing that won't change all that much is that ruinous light pollution, captured by Nik Szymanek, above.
Know what's causing it? That's Mars!
If you want to see more, and you can't wait for the information to unfold, there are two things I recommend you check out. First, David Bishop has some early photos on his site, where you can find before-and-after photos of Messier 95.
And if you need more right now, Deep Sky Videos has put together a wonderful presentation -- released just yesterday -- on this supernova so far.
So if you can find Mars, and you have a good enough telescope and good enough skies, you can be among the first to see the latest supernova in our night sky!
Update: The supernova has been confirmed! It's a Type IIp supernova, and its name is SN 2012aw! It will brighten, and continue to be visible probably into June, when Mars will have (finally) moved a considerable distance away. Keep watching!Read the comments on this post...
So, this is the new book from the authors of Why Does E=mc2?, covering quantum mechanics in a roughly similar manner. This book, or, rather, Brian Cox talking about some material from this book, created a bit of controversy recently, as previously discussed. But other than that, Mrs. Lincoln, how did you like the play?
The big hook here is that they set out to discuss quantum mechanics for a popular audience using a Feynman-type picture from the very beginning. This is an intriguing idea, and sort of appealing in the same basic way that Sakurai's famous graduate text in quantum mechanics and Townsend's undergraduate version appealing. Those books are interesting because they come at the subject from a different angle, formulating everything first in terms of spin-1/2 particles, rather than wave mechanics. This makes certain types of problems much easier to deal with, and lets students see the subject in a very different light.
So, the general idea of a book on quantum physics that starts with Feynman's path integral formulation of the theory-- other than, you know, Feynman's own book on QED-- is an interesting idea. The Feynman approach is the starting point for a lot of modern approaches to the theory, and looks very different than the Schrödinger wave mechanics most popular treatments (my own included) take. I got some useful stuff out of their book on relativity, so I was hoping for some useful insights from this one.
Like its predecessor, though, I want to like this book more than I do.Read the rest of this post... | Read the comments on this post...
A couple of cool items in the promotion of How to Teach Relativity to Your Dog:
-- A little while back, I spoke to Alan Boyle, who writes the Cosmic Log blog for MSNBC, who posted a very nice story about the book last night. Mainstream media, baby!
It also uses this very cool picture of Emmy and me in my lab:
(Many thanks to Matt Milless for taking that and a bunch of others.)
-- This weekend (either Saturday or Sunday, depending on where you are), I'll be on the Science Fantastic radio show, talking about relativity with Michio Kaku. There's a lsit of stations that carry it linked from that page, or you can listen online (this site purports to let you stream it, but I haven't tried yet.Read the comments on this post...
"To use Newton's words, our efforts up till this moment have but turned over a pebble or shell here and there on the beach, with only a forlorn hope that under one of them was the gem we were seeking. Now we have the sieve, the minds, the hands, the time, and, particularly, the dedication to find those gems--no matter in which favorite hiding place the children of distant worlds have placed them."
-Frank Drake and Dava Sobel Looking up at the canopy of stars in the night sky, and realizing that each point of light is a star system not so unlike our own, one can't help but wonder about those extraterrestrial worlds that we know exist around a tremendous fraction of them.
(Image credit: Tom's Eye on the Sky.)
With hundreds of billions of stars and (possibly) upwards of a trillion planets, it's been known for a very long time that there's a definite, real chance that other intelligent life exists right now in our own galaxy.
For decades, we've broadcast radio messages out into space, and built giant arrays of radio telescopes, searching for those same types of signals originating from other sources in the night sky.
(Image credit: VLA in Socorro, New Mexico, retrieved from here.)
Of course, this is a tremendously ambitious task. Even a very intense radio signal will lose its power the farther away from it you are. The problem, of course, is that each time you double the distance away from a radio transmitter, you pick up only one-quarter of the intensity you would have received at a closer distance.
(Image credit: Arthur's Clip Art.)
Even special setups that collimate the beam -- assuming, for example, that an alien species had the idea to point their beam directly at us -- still suffer from this. Even the best setups for beam collimation of light still wind up having the signal spread out over a substantial angle, and still suffers from the problem that the farther away you are, the less intensity you receive squared: a radio transmitter ten times as far away needs to be a hundred times as powerful for you to pick up the signal.
(Image credit: Chris Long.)
It's difficult to imagine that a civilization-generated signal located thousands of light-years away, across the galaxy, would be able to outshine the cosmos by time it reached us.
But we do have one sterling example of a beam we can collimate to an outstanding precision: beams of extremely high-energy particles!
(Image credit: Maximilien Brice, 2009.)
A pulse of high-energy particles, such as the kinds we create at the Large Hadron Collider, above, achieves speeds around 99.9999% the speed of light, more closely collimated than even the beam from a laser. Now, we sometimes receive high-energy particles -- originating from space -- here on Earth. When we do, how do we identify them?
(Image credit: Randy Russell using a photo via UCAR / Nicole Gordon.)
They strike the Earth's upper atmosphere, producing a shower of particles. Neutrinos and muons make it to the ground, where -- if we're lucky and prepared -- we can identify them. Launched from Earth, however, the charged particles would certainly hit the atmosphere on the way out. And since muons are unstable, by time they arrived at their destination, the only recognizable signal would be the neutrinos!
In other words, if we wanted to send a signal to an alien world, alerting them to our presence, our best bet would be to send them collimated, patterned pulses of neutrinos!
(Image credit: Jerry Ehman, republished from Smithsonian Magazine.)
What's remarkable about this -- even though it wasn't the experiment's intention -- is that we just demonstrated the ability to detect exactly this type of signal!
(Image credit: MINERvA team / University of Rochester.)
Last week, scientists announced -- for the first time -- that they sent a neutrino signal through the solid rock of the Earth, in binary morse code, and received it at a neutrino detector over a kilometer away!
(Image credit: MINERvA Collaboration.)
Despite the fact that only one out of every ten billion neutrinos can be detected in an apparatus like the MINERvA detector, above, and that the effective transmission rate was only one bit every ten seconds, by repeating the message many times, the detector was able to build up the binary pattern of zeroes and ones, eventually decoding the binary message!
(Image credit: D.D. Stancil et al.)
What was the message? Why, the name of the particle itself: N-E-U-T-R-I-N-O.
If someone, thousands of light years away, is sending a repeating neutrino signal towards us, we've just demonstrated the capability of detecting and identifying exactly that type of communication.
The signals of intelligent life could already be there. We just need to listen in the right way, and neutrinos might be the answer!
(Also, a big thanks to Randall for the elegant new blog banner; hope you like it!)Read the comments on this post...
I'm trying not to obsessively check and re-check the Dog Physics Sales Rank Tracker, with limited success. One thing that jumped out at me from the recent data, though, is the big gap between the book and Kindle rankings over the weekend. The book sales rank dropped (indicating increased sales, probably a result of the podcast interview), while the Kindle rank went up dramatically. This suggests that people who listen to that particular podcast are less likely to buy new books on the Kindle than new books on paper.
This got me wondering, though, whether this was an anomaly, or a general truth. That is, is there any correlation between the sales rank of the paper edition of a book and the sales rank of the Kindle edition of the same book? Happily, the sales rank tracker spits out all the hourly rankings in a nice table that I could copy into SigmaPlot and crank away on, producing the following:
This is a plot showing the Kindle sales rank of How to Teach Relativity to Your Dog (vertical axis) versus the sales rank of the paper edition (horizontal axis). I smoothed the hourly data a bit, averaging together five hours, because it's really noisy, but that makes almost no difference.
What does this say? Well, that there's a pretty weak correlation between them. The data points fall more or less in a wedge extending up and to the right, which tells you that when one is really high, the other tends not to be very low, and when one is low, the other also tends to be low, but the relationship between them is pretty weak. At a book rank of about 25,000, the Kindle rank ranges from about 14,000 to about 96,000.
This is for the recently released book, though. Maybe more data would make a clearer picture? In a word, no. In a thousand words (i.e., one picture):Read the rest of this post... | Read the comments on this post...
I've done a bunch of publicity stuff for How to Teach Relativity to Your Dog, some of which frustratingly continue to not appear yet, but one thing from this week has gone live: a podcast interview on the Matt Lewis Show, where I talk about why and how I explain physics to the dog, and a little bit about why relativity is cool.
I continue to struggle a bit with the fact that relativity is a very visual subject-- most of the best explanations involve pictures, which aren't much help in an audio-only medium. I had trouble with this at Boskone, too-- when I was doing a reading, it was hard to find a section to read that didn't involve a lot of diagrams. And I still tend to go on a little too long in my descriptions. It went all right, though, and Lewis gets points for being the first person I've talked to about this to get my description of the dog voice as "a sort of Andy Kaufman 'Foreign Guy' thing."
So, if you've got 15 minutes to kill, check it out.Read the comments on this post...
"The saying 'It's not over 'til the fat lady sings' is erroneous, because women who are fat are never listened to." -Margaret Cho Last year, the OPERA collaboration made worldwide headlines when they announced the results of a remarkable experiment.
(Image credit: OPERA / CERN.)
From over 730 kilometers away, in another country, neutrinos were created by one of the most powerful particle accelerators in the world. Protons at over 99.999% the speed of light were smashed into matter, creating a highly collimated beam of neutrinos, which was launched through the Earth at, presumably, speeds indistinguishable from the speed of light.
Underground, beneath the Italian mountain of Gran Sasso, laid the huge OPERA detector, capable of detecting these high-energy neutrinos.
(Image credit: OPERA / INFN / CERN.)
But what it was also able to do, so they claimed, was to measure the timing of these neutrinos so accurately as to be able to test Einstein's theory of special relativity!
As you well-know, nothing is supposed to be able to move faster than the speed of light in a vacuum. Nothing. Which is why it was absolutely shocking when they released their first results.
(Image credit: OPERA Collaboration; T. Adam et al.)
60 nanoseconds early, they said, their neutrinos arrived. This wasn't an error, either, they said, as their uncertainties were only around 10 nanoseconds. And if that was true, over the distances they were talking about, that means these neutrinos would be moving something like 7,500 m/s faster than light, which is huge!
As we've said many times, claims like these, that are extraordinary, require evidence that is also extraordinary. So I was very excited to report that, in short order, we were going to either confirm or refute OPERA's claims!
But another experiment, one that had come out earlier and challenged OPERA's results, had other plans. You see, OPERA had recently announced that they had uncovered two potential problems with their experiment -- the loose cable and a possible timing miscalibration -- which threw their results into doubt.
What it really meant, if you look up at the image of their claimed results, is that their claimed errors, which were tiny, should have actually been much larger due to those issues.
(Image credit: Matt Strassler.)
This is a problem that plagues a great many experimental and observational sciences: fully accounting for your systematic errors. After all, it is difficult to account for uncertainties and / or errors due to something you were simply expecting would work properly! You account for systematics based on all the errors you can reasonably anticipate, but once those are over and done with, you stop counting. But when an unexpected error does happen, and you weren't expecting it, it can lead you to have an undue amount of false confidence in what are actually insignificant results.
And it was the ICARUS team -- another neutrino detector underneath Gran Sasso -- that set out to show that OPERA had done exactly that. Intending to refute the OPERA team's results, ICARUS has gone out to set the record straight about Einstein's relativity.
(Image credit: the ICARUS-T600 detector installed in LNGS - HallB, retrieved here.)
Evoking shades of Ethel Merman, ICARUS basically said to OPERA, "Anything you can do, I can do better." And, over practically the same baseline, using the same energy neutrinos created from the same proton beam, ICARUS set out to re-test the OPERA experiment.
(Image credit: the latest ICARUS paper; M. Antonello et al.)
Except, you know, without the errors. And what they found should put the whole issue to rest. The OPERA neutrinos, you'll remember, arrived around 60 nanoseconds early, with an originally claimed uncertainty of 10 ns. The ICARUS results, making the same measurements with different equipment?
(Image credit: the latest ICARUS paper; M. Antonello et al.)
It means that, combined with ICARUS' earlier results, we can constrain that not only are neutrinos of this energy not moving at the speed OPERA concluded, but they must be moving much closer to the speed of light than OPERA's original results would have indicated.
And that's pretty much the end of the line for these faster-than-light neutrino claims. It will be interesting to see what OPERA's next results are, as well as what MINOS and T2K have to say, but with the ICARUS results in and the OPERA uncertainties known to be much larger than originally claimed, there's suddenly no reason to believe that neutrinos move faster-than-light at all.
And if you were skeptical the whole time, good for you. The extraordinary evidence you were waiting for just came in, and it's the sound of the fat lady singing!Read the comments on this post...
A little more tab clearance, here, this time a few recent stories dealing with those elusive little buggers, neutrinos. In roughly chronological order:< /p>
- The Daya Bay experiment in China has measured a key parameter for neutrino oscillation (arxiv paper), the phenomenon where neutrinos of one of the three observed types slowly evolve into one of the others. Mathematically, this is described as each of the three types we observe being an admixture of three more fundamental types. This mixing is described in terms of the sine of some "mixing angle," because physicists love geometry, and two of the three mixing angles had already been measured. The Daya Bay experiment measured the third-- or, more precisely, they found that the square of the sine of the third mixing angle is 0.092 +/- 0.016 +/- 0.005, where the two uncertainty values are for statistical and systematic uncertainties. This is somewhat larger than expected, which is probably a good thing, because it may imply more of a difference between matter and antimatter than you get from the simplest models, which in turn would help explain why everything we see in the universe is matter and not antimatter.
- A group at Fermilab has sent a message via neutrinos (press release), encoding a simple signal in on-off pulses of neutrinos generated at Fermilab and detected by a giant underground detector a kilometer away. This is not particularly useful for anything, because they need a big particle accelerator to make the pulses and a detector with a mass on the order of tons to detect them, but it's kind of cute.
- Finally, a second group at the Gran Sasso laboratory in Italy has used the same neutrino beam used by the OPERA collaboration to check the time of flight of the neutrinos passing from CERN to Italy, and find that it agrees perfectly with what you expect for neutrinos moving at light speed, not the tiny bit faster that OPERA saw. As usual with particle physics stuff, Matt Strassler has a good and balanced round-up. These results from the ICARUS experiment (I'm not even going to try to figure out what linguistic crimes they committed to get that acronym) are fairly conclusive evidence that OPERA's result was in error, though given the complexity of both measurements, it's still worth repeating the experiment as planned in May.
And that's the news regarding the elusive neutrino.Read the comments on this post...
One Year After Fukushima, a Startup Named Kurion Continues to Shed Light on What it Means to Live in the Nuclear Age [USA Science and Engineering Festival: The Blog]
By Larry Bock
Founder and organizer, USA Science & Engineering Festival
When searching for a prime, real-life example of how science and technology are making a difference in the world right now, my thoughts lately turn to a small but feisty greentech startup that you may never have heard of: Kurion, Inc.
Based in Irvine, CA with 15 employees, this profitable three-year-old company which specializes in nuclear waste cleanup has quietly and effectively been using its technology at the front lines of Fukushima, the site of what is being called one of the largest nuclear disasters in history. Weeks after the unforgettable earthquake and ensuing tsunami struck Japan last year which caused emissions of nuclear contaminants to be released into the air from reactors at the Fukushima Daiichi Nuclear Power Station, Kurion was selected to join a group of multi-billion dollar companies to help clean seawater that was being pumped into the reactors to cool them down.
Within three weeks of first contact, TEPCO authorized Kurion's proposed solution to the challenge. Eight weeks later, Kurion's system had been designed, built, air freighted by three Russian Antonov transports, installed and was fully operational removing more than 99.9% of the seawater radioactivity of greatest concern. Other companies which were awarded contracts by the Japan utility TEPCO to aid in this challenging duty were France's AREVA, Japan's Hitachi-GE Nuclear Energy and Toshiba. Of these, only Kurion and AREVA were able to deliver systems in time to prevent the highly contaminated seawater from overflowing the limited available tankage into the ocean and of these only Kurion continues to operate today.
Kurion stands out as the only startup selected -- and for good reason: the firm for a while has been developing a material called "ion specific media" that greatly improves the way cleanup technology is deployed to soak up nuclear particles and as a result shrink the radioactive material down to a small manageable size. The resulting waste stream, an inorganic powder, can further be turned into glass (a standard industry process known as vitrification). Kurion's innovation brings a more modular approach to the vitrification process, so the clean-up technology can be quickly adapted and installed in the contaminated spill site. Add to that Kurion's team composed of nuclear waste industry veterans, and you'll understand why the company was able to enter a direct contractual arrangement with TEPCO.
Since last June, says Kurion's CEO John Raymont, the company's technology has been used as part of what he calls "an unprecedented external reactor water cooling system," designed to replace Fukushima's in-plant reactor water cooling mechanism until the reactor's original nuclear cores can be removed. Bottom line: Kurion's presence at Fukushima is helping to mitigate radiation contamination to humans and the environment, dramatically turning a disastrous situation around.
As the first anniversary of the Fukushima disaster past on March 11th, Kurion and the cleanup are perfect examples of how science and technology are making a difference where it matters around the world. In my opinion, it illustrates in realistic terms what it means to be human in the nuclear age -- with all the benefits and risks nuclear power brings.
To help get this message across, we are proud to include Kurion and its representatives as key participants in the upcoming USA Science & Engineering Festival hosted by Lockheed Martin, the nation's largest celebration of science and engineering. The Festival is on a mission to inspire the next generation of innovators by reinvigorating the interest of our nation's youth in science, technology, engineering and math via hands-on presentations with experts that motivate, compel, excite, entertain as well as educate.
Kurion's participation is especially exciting for me for a couple of reasons. As a startup entrepreneur myself before establishing the Festival several years ago, I co-founded or financed the early stage growth of 40 companies in the life and physical sciences from inception, so I know well of the rigors and challenges that Kurion has and continues to experience to further establish itself in the competitive field of technology. Second, at Lux Capital (one of two venture capital firms backing Kurion), I serve as Chairman of Lux's Advisory Board of industry experts where we are all extremely proud of Kurion's success.
Join visitors at the Festival Expo on April 28-29, 2012, in Washington, DC when we take you inside the power of nuclear energy (along with other exciting areas of science and engineering) with such experts as Kurion, the U.S. Department of Energy, the University of Massachusetts Lowell Physics Department, and the ATLAS Experiment at the Large Hadron Collider who are all helping to make our co-habitation with nuclear power safer and more beneficial. Here is just a sampling of what you'll discover:
How Kurion is Cleaning Up Fukushima -- From Kurion, learn how they perform remediation on contaminated water and stop the spread of radioactive isotopes at Fukushima and other sites. Kurion experts will also demonstrate how an ion-exchange column works and how they trap dangerous particles using their 3-D vitrification simulator.
Future Implications of the Fukushima Disaster -- Meet and hear Fred Bortz, Ph.D., who is among our Featured Authors at the Expo's Book Fair. A physicist-turned-writer, Bortz (whose science training includes three years in nuclear core design), is the author --among other works -- of the recent book, Meltdown: The Nuclear Disaster in Japan and Our Energy Future, which sheds light on the future of nuclear and what the next generation will face in dealing with its development.
Real-Life Applications: From National Defense to Biomedical Photonics -- Learn from these experts: how the U.S. Department of Defense is developing solutions that protect first responders from potential nuclear, radiological, chemical and biological threats; how renowned physicists from the University of Massachusetts Lowell are making life-saving advances in areas ranging from nuclear physics and radiation science to biomedical photonics, and from the American Nuclear Society how to compute your own annual radiation dose.
The Wonders of the Large Hadron Collider (LHC) -- Scientists from the ATLAS Experiment at the LHC take you inside the wonders of the world's largest and highest-energy particle accelerator which was developed over a 10-year period to probe new frontiers in high energy physics including the origins of the universe.
How the DoE is Impacting Climate and Energy Solutions -- Department of Energy scientists from its Atmospheric Radiation Measurement (ARM) facility will demonstrate how its measurements are bringing science solutions to the world, including improving climate models, and researchers from the Department's Berkeley National Laboratory will shed light on how they are developing new approaches to energy by studying infinitesimal particles at the sub-atomic level.
Radiation Physics in 3-D -- Enter a 3D virtual treatment room with experts from the American Association of Physicists in Medicine and learn how a radiation treatment accelerator works. See how medical physics and science are used in the radiation treatment of cancer. Participants will get a 3D view of the technological advances used in this cancer treatment.
Nuclear power, the byproduct of our existence in the modern age, is here to stay. Join us at the Festival as we explore how to coexist with it responsibly and safely for the benefit of all. For more on the Festival, visit: http://www.usasciencefestival.org/
Read the comments on this post...
"Now go on, boy, and pay attention. Because if you do, someday, you may achieve something that we Simpsons have dreamed about for generations: you may outsmart someone!" -Homer Simpson Today, March 14th, is known tongue-in-cheek as Pi Day here in the United States, as 3.14 (we write the month first) are the first three well-known digits to the famed number, π. As you know, it's the ratio of a perfect circle's circumference to its diameter.
(Image credit: LeJyBy at Flickr Creative Commons, retrieved here.)
It's also very, very, very hard to calculate exactly, because it's impossible to represent π as a fraction. (You may remember that's part of the definition of an irrational number.) But that doesn't mean we haven't tried!The easiest way to try is to either inscribe or circumscribe a regular polygon around a circle of radius 1, and calculate the polygon's area. The more sides you make, the closer you'll get.
(Image credit: Archimedes' Pi approximation, by Leszek Krupinski.)
Archimedes, who discovered the fraction 22/7 (which is why Pi Day is July 22 in Europe), took the equivalent of a 96-sided polygon to do this, and found that π was between 220/70 and 224/71, which is not bad for two thousand years ago!
But it's hardly the most impressive approximation for π from back then. That honor goes to the Chinese mathematician, Zu Chongzhi.
(Image credit: Statue of Zu Chongzi in Tinglin Park in Kunshan, by Gisling.)
He discovered -- in the 5th Century -- the approximation Milü, which is 355/113. Which is equal to, for those of you at home, 3.1415929... meaning you have to go to the eighth digit to see the difference between this number and π. In fact, if we look at the best fractional approximations of π...
(Image credit: Gisling.)
we wouldn't find a better one until 52163/16604! (Exclamation point, not factorial!) That was the world's best approximation for π for something like 900 years, until this guy came along. Pretty impressive!
But what if you wanted to calculate π, but wanted to do as little math as possible? No geometry, just basic counting and four-function mathematics? Well, if you can play darts, you can do it!
It will only get you to π very slowly, but throwing darts (randomly) at a circle with a square of area equal to the circle's radius will allow you to calculate π! How so? Count the darts that land in the circle, divide by the number of darts that land in the square, and that's how you calculate π. (For those of you who write a computer program that can do this, congratulations, you've just written your first monte carlo simulation!)
But let's say you wanted to be more efficient, but you wanted to get to π with arbitrary accuracy, given enough time. Have I got a fun method for you: you can represent it as a continued fraction, and the farther you continue it, the more accurate you'll get!
For example, here's the results from the first few terms; not bad!
Pi Day is also a special day for anyone interested in astronomy and space! Four famous astronomy and space heroes have their birthday on Pi Day; can you name them all from their pictures?
(Okay, okay, one of them is easy!)
As far as the pies go, I'm still no good at making pie crust, but I do have a special treat that I can make, with a circumference and a diameter and everything.
(Image credit: Jemma.)
Yes, it's a Leche Flan! Hope your day is as sweet as they come, hope that you enjoyed all the fun facts about pi, and if you're up late over the next couple of nights, enjoy the Pi Day miracle of the Jupiter-Venus conjunction in the night sky!
(Image credit: Laurent Lavedar, TWAN, retrieved from National Geographic.)
Happy Pi Day!
(And your birthday boys are, from L-R, Albert Einstein, Apollo 8 Commander Frank Borman, Astronomer Giovanni Schiaparelli, and last-man-on-the-Moon Gene Cernan.) Read the comments on this post...
One of the things that made me very leery of the whole Brian Cox electron business was the way that he seemed to be justifying dramatic claims through dramatic handwaving: "Moving an electron here changes the state of a very distant electron instantaneously because LOOK! THE WINGED VICTORY OF SAMOTHRACE EINSTEIN-PODOLSKY-ROSEN PAPER!" On closer inspection, it's not quite that bad, though it takes very close inspection to work out just what they are claiming.
That said, though, it's fairly common to hear claims of the form "when two particles are entangled, anything you do to one of them changes the state of the other." This is not strictly true, though, and it's worth going through in detail, if only so I have something to point to the next time somebody starts using that line. This will necessarily involve some math, but I'll try to keep it as simple as I can.
So: the problematic claim is that doing things to one particle of an entangled pair of particles affects the state of the other particle in the pair. This is true only for a very small subset of "doing things" and "affects the state"-- that is, it is absolutely and unequivocally true that measuring the state of one entangled particle in some basis determines the possible outcomes of measurements on the other particle in the pair. However, the vast majority of things you might do to one of the two particles do not produce corresponding changes in the state of the other. In fact, most of the things you might do will appear to destroy the entanglement altogether.Read the rest of this post... | Read the comments on this post...
"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." -Albert Einstein Last month, an interesting conversation happened on the topic of the most difficult course that a student takes in their studies.
(Image credit: Steve Perrin / University of Michigan MSIS.)
The question, of course, was asking about most difficult in terms of the course content that the student must learn. In any field, there are plenty of options to choose from, and while an individual student's mileage may vary, teachers and professors tend to learn very quickly just which courses (and what course material) students have the most difficulty gaining a working understanding of. On that topic, I have to agree with Chad that, for an undergraduate physics major, the advanced electromagnetism course is the toughest.
(Image credit: Mike Willis.)
But I thought it'd be much more interesting -- on behalf of all teachers at all levels -- to take on the following question: What is the most difficult course to teach? Having taught a huge variety of courses over my life, ranging from public secondary school to high school to public and private Colleges and Universities, I have to say that the courses with the most difficult content are by no means the most difficult courses to teach.
In my experience, the most difficult course to teach is the one where you, the teacher, cannot control what or how you are teaching.
(Image credit: Mr. Lawrence / Eagles4Kids.com.)
There are a handful of qualities that are basically required of an individual to be a good teacher; qualities for which there are no substitute. A good teacher -- in my experience -- must be:
- Competent: with the curriculum/subject matter that they're teaching,
- Attentive: to the skill level, needs, and abilities of the students,
- Prepared: to explain, demonstrate, and challenge students in a variety of ways,
- Empowered: to teach the material in whatever way, however unorthodox or creative, they see fit, and
- Self-aware: of their own strengths, weaknesses, abilities and limitation.
Let me share two important secrets with you.
(Image credit: Eric Joselyn, retrieved from thenotebook.org.)
1.) There is no amount of control you can take away from a bad teacher that will turn them into a good teacher.
2.) There is nothing worse you can do to a good teacher than take away their autonomy as to how and what they teach to their students in their classrooms.
That's it. We've all had experiences of good and bad teachers that have been seared into our memories, but all of my best experiences would never have happened if my education was as micromanaged as many classrooms are today.
And that's truly a shame. Because the best courses I've ever taught are -- at least from my perspective -- college-level introductory astronomy and the advanced electromagnetism course mentioned above.
(Image credit: Chris Proctor, retrieved from here.)
For both of those courses, I had complete creative control over everything: the material covered, the assignments, the exams, etc. I could take the journey that I not only chose with my students, I could tailor that journey to their needs and abilities, my strengths, and all the other obligations and necessities that came up.
And we had a ball. They got to learn skills and take on challenges that they wouldn't have been confronted with anywhere else; they got an experience that was unique to having me as their teacher. And it was a joy, for me, too. On the other hand...
(Image credit: MemeCenter.com / Austin Powers.)
what was the most difficult course I've had to teach? That would have to be the introductory physics course geared towards non-majors. The curriculum is simply too rigid and comprehensive to do a high-quality job in the time allotted to do it. It is a curriculum that has been unreasonably standardized for the skill level of most students. As a result, a teacher is either forced to skip many important topics that students will be held responsible for, or to expose the students to a great deal of material without the time necessary to teach for mastery. Either way, it's a losing proposition, and one that a great many teachers (and students) resent.
If you want your children to get the highest quality education possible, don't forget this lesson. Demand competent, attentive, prepared and self-aware teachers, and make sure you empower them to do the best job that they can do!Read the comments on this post...
Imagine a car small enough for a dust mite. Crazy, right?Read the rest of this post... | Read the comments on this post...
I finally got a copy of Cox and Forshaw's The Quantum Universe, and a little time to read it, in hopes that it would shed some light on the great electron state controversy. I haven't finished the book, but I got through the relevant chapter and, well, it doesn't, really. That is, the discussion in the book doesn't go into all that much more detail than the discussion on-line, and still requires a fair bit of work to extract a coherent scientific claim.
The argument basically boils down to the idea that the proper mathematical description of a universe containing more than one fermion is a many-particle wavefunction that is overall antisymmetric under the exchange of any two electrons. That is, if you numbered every electron in the universe, you would write the wavefunction down one way, and if you swapped the numbers on two of the electrons, then re-wrote the wavefunction, you would get the same thing you had the first time, but with an overall negative sign. Thus in seeking to make a quantum model of a hydrogen atom in your living room, you would need to write down some sort of 1090x1090 Slater determinant (or whatever the actual total number of electrons in the universe is) to get the proper state of the many-(many-many-many...)-body system. The total energy of this state will depend on the energy of all of the individual electrons, and some complicated overlap integrals between every single electron state and every single other electron state, so I hope you have a lot of paper or a really fast (quantum?) computer to help you work it out.Read the rest of this post... | Read the comments on this post...
Seems like all the action is in Norway these last few years...
Meteorite crashes through roof in Oslo
from Verdens Gang
Fist size meteorite smashes through roof in Oslo suburb
Nice looking chunk - be worth a pretty penny, as one of the few meteorites with confirmed provenance of hitting a structure.
see also Fireball over Norway - at VG
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By Joe Schwarcz PhD, Author, USASEF Expo Performer, AT&T Sponsored Nifty Fifty Program Speaker
Yellowstone National Park's iconic "Old Faithful" geyser is pretty faithful. It can be counted on to erupt every 50-90 minutes. Iceland's "Great Geysir," from which all other geysers get their name is less reliable. It was mostly dormant for sixty five years before it began semi-regular eruptions again in 2000 thanks to an earthquake. But in New Zealand, you can set your watch by the eruption of the Lady Knox Geyser, named after a former Governor of the country. At exactly 10:15 AM every day a spectacular plume of water and steam bursts into the air to a height of up to twenty meters. How can a natural phenomenon be so predictable? Well, in this case nature gets a little help from chemistry.
At the appointed time, a detergent solution is poured down the channel from which the water erupts. This has the effect of reducing the surface tension of the water that deep within the shaft has been heating up to boiling temperatures due to underground volcanic activity. Surface tension refers to the attractive force between water molecules, and is in fact responsible for water being a liquid at ordinary temperatures. Liquids are characterized by the close proximity of their component molecules, while in gases the distance between molecules is much greater. If the surface tension of a liquid is decreased, the H2O molecules can separate from each other with greater ease, with the result that the liquid turns into a gas. Molecules of "surfactants," a class of substances that encompasses soaps and detergents, wiggle their way in-between water molecules, allowing the boiling liquid to instantly turn into steam. The steam then forces the water that has collected in the channel to burst upwards, and we have an eruption.
The possibility of making a geyser erupt artificially was discovered by accident in New Zealand in 1901 when an "open prison" was established at Waiotapu for criminals who were deemed not to be a danger to society. It so happens that this is one of the most volcanically active areas of the world and the prisoners took advantage of the hot water seeping up from the natural thermal springs to wash their clothes. One day one of them must have used just the right amount of soap and triggered an eruption when the soap solution found its way down the fissures in the rock into the chambers in which underground water had pooled. This is the concept used today to stimulate eruption of the Lady Knox Geyser although detergents have replaced soap because they have been found to be less damaging to the geyser's internal natural plumbing. On occasion Iceland's Great Geysir has also been "soaped" but this is now prohibited for environmental concerns.
Long before the prisoners made their accidental discovery, the science of geyser eruptions had been worked out by none other than Robert Bunsen, of burner fame. Actually Bunsen did not invent the famous burner but did improve upon existing equipment by showing that mixing the combustible gas with just the right amount of air led to a high temperature non-luminous flame. Such a flame was very useful in the development of Bunsen's most famous discovery, the spectroscope. In collaboration with physicist Gustav Kirchoff, Bunsen designed an instrument that would pass the light emitted from a sample heated by his burner through a prism. The "spectrum" of light produced was found to be characteristic of the element found in the sample. Before long Kirchoff and Bunsen had identified cesium and rubidium as new elements and paved the way to the identification of thallium, indium, gallium, scandium by others through spectroscopy.
In 1845, during his tenure as Professor of chemistry at Marsburg University, Bunsen was invited by the Danish government on a geological trip to Iceland following the eruption of Mount Hekla. Bunsen had a lifelong interest in geology and used the occasion to study the gases released from volcanoes and performed analyses on volcanic rocks. He also became interested in Iceland's abundant geysers, especially "The Great Geysir" that propelled water to a height of some fifty meters. Bunsen hypothesized that eruption occurred when a column of underground water was heated around its middle by volcanic activity. In the true spirit of science, Bunsen constructed an artificial geyser in the laboratory consisting of a basin of water from which a long tube filled with water extended upwards. He heated the tube at various points and showed that it was when the water in the middle reached its boiling point that an eruption occurred just like in a natural geyser.
Geysers can do more than excite tourists. In Iceland hot water from geysers is used to heat homes and warm greenhouses, allowing food to be grown in an otherwise inhospitable climate. The accumulation of steam deep within the ground that makes geysers possible can also be tapped by geothermal power plants to produce electricity. Geothermal energy is a great source of electricity but drawing off the steam can lead to the destruction of geyser activity.
Not all geysers gush steam and hot water. In the case of cold-water geysers the eruptions are driven by carbon dioxide gas that forms as limestone, calcium carbonate, decomposes. The gas becomes trapped in underground aquifers until it builds up enough pressure to explode towards the surface through cracks in the strata propelling water into the air. Some of the gas remains in the water in the form of small bubbles so that the geyser actually dispenses soda water.
If you want to experience a mini-cold-water geyser, just drop a couple of Mentos into a bottle of Diet Coke. But do it outside. It makes a mess. If you use a special tube (available from Steve Spangler Science) that can simultaneously drop 7-10 Mentos into the bottle, you'll be treated to a true spectacle as the liquid bursts to the stunning height of about ten meters. That's still some 490 meters short of the super eruptions once produced by the Waimangu Geyser in New Zealand between 1900 and 1904 before the natural plumbing was destroyed by a landslide. The world's tallest geyser now is Yellowstone's Steamboat Geyser that propels water some ninety meters into the air. Unfortunately its eruptions are not predictable. Except on YouTube.Read the comments on this post...
The Links Dump item about software patents this morning includes a lament that there are so many silly little software patents, organized so badly, that finding one you might be infringing would take forever. This may or may not be a convincing argument against them, but for a physics geek like me, my first reaction was "You just need a quantum computer running Grover's algorithm for searching an unsorted database." And I suppose there's a background element for a satirical SF novel in that-- quantum computers ultimately being developed not by banks or the NSA, but by lawyers looking to speed the process of document discovery.
Of course, this in turn reminded me that I have a bunch of quantum-related tabs open in Chrome, and I really ought to do something with those. So, here's a special quantum-themed links dump sort of post:
-- Scott Aaronson, a noted critic of the quantum computing claims by D-Wave, who famously (well, nerd-famously) declared their supposed quantum processor about as useful as a roast beef sandwich, made a visit to their facility, and moderates his stance somewhat.
-- Every few weeks, there's a story about some new promising quantum computing technology. The most recent is the demonstration of topological error correction, which might be essential for making quantum processors that can withstand the noise that inevitably creeps into any real system. This would be good fodder for a ResearchBlogging post, if I had the time to understand it in detail, but I don't. So you get this passing mention.
-- Matt Leifer has written another article about the theorem ruling out some kinds of interpretations that made a bunch of news a little while back. It's for the "Quantum Times," the newsletter of an APS group on quantum information, so it's not exactly at the level your dog might want to read, but if you know a little about it, and want to know more, it's a good piece.
And that's three browser tabs closed. Only 20-odd left...Read the comments on this post...